Tutorial 2 Feb 2016

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TUTORIAL 2- BNJ 10203 STATICS

Statics BNJ 1020

F i Pl (2D

TUTORIAL 2

Arahan :

Pelajar dibahagikan dalam kumpulan bertiga-tiga.

Kumpulan 1, 10 menjawab soalan - 2-1, 2-9 , 2-17, 2-25, 2-33

Kumpulan 2, 11 menjawab soalan - 2-2 , 2-10 , 2-18, 2-26, 2-34








Setiap pelajar perlu menghantar jawapan tutorial (Tulisan Tangan) ini pada

minggu berikutnya iaitu kelas berikut.

Sekian.

SKEMA MARKAH/ RUBRIK :

a. Semangat kerja berkumpulan : 10%

b. Kepimpinan yang baik/ ahli pimpinan yang baik : 10%

c. Komunikasi yang baik diantara pensyarah, pemimpin

& ahli pimpinan : 10%

d. Jawapan soalan yang tepat : 10%

TUTORIAL TAHAP CLO-PLO

FUNCTION INDIVIDUALLY

OR IN TEAM, EFFECTIVELY

IN PROBLEM SOLVING

15% (A3, PLO5)

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Statics BNJ 1020

F i Pl (2D

Problem 2-1

Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured

counterclockwise from the positive x axis.

Given:

F1 600N

F2 800N

F3 450N

α 45deg

β 60deg

γ 75deg

ANS: FR = 867N

φ 108 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-2

Determine the magnitude of the resultant force and its direction measured

counterclockwise from the positive x axis.

Given:

F1 80N

F2 60N

θ 120deg

ANS:

FR 72.1 N

β 73.9 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-4


counterclockwise from the positive u axis.

Given:

F1 300N

F2 500N

α 30deg

β 45deg

γ 70deg

ANS : FR 605 N

φ 85.4 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-5

Resolve the force F1 into components acting along the u and v axes and determine the

magnitudes of the components.

Given:

F1 300N

F2 500N

α 30deg

β 45deg

γ 70deg

ANS: F1u 205 N

F1v 160 N

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Statics BNJ 1020

F i Pl (2D

Problem 2-6



Given:

F1 300N

F2 500N α

30deg

β 45deg

γ 70deg

ANS : F2u 376 N

F2v 482 N

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Statics BNJ 1020

F i Pl (2D

Problem 2-7

Determine the magnitude of the resultant force FR = F1 + F2 and its direction measured

counterclockwise from the positive u axis.

Given: F1 25N

F2 50N

θ1 30deg θ2

30deg θ3 45deg

ANS : FR 61.4 N θ 6.85 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-8

Resolve the force F1 into components acting along the u and v axes and determine the components.

Given:

F1 25N

F2 50N

θ1 30deg

θ2 30deg

θ3 45deg

ANS: Fu −12.9 N

Fv 35.4 N

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Statics BNJ 1020

F i Pl (2D

Problem 2-9


components.

Given:

F1 25N

F2 50N

θ1 30deg θ2

30deg

θ3 45deg

ANS:

Fu 86.6 N

Fv −50 N

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Statics BNJ 1020

F i Pl (2D

Problem 2-10

Determine the components of the F force acting along the u and v axes.

Given:

θ1 70deg

θ2 45deg

θ3 60deg

F 250N

ANS: Fu =320N

Fv =332N

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Statics BNJ 1020

F i Pl (2D

Problem 2-11

The force F acts on the gear tooth. Resolve this force into two components acting along the lines

aa and bb.

Given:

F 20N

θ1 80deg

θ2 60deg

ANS :

Fa 30.6 N

Fb 26.9 N

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Statics BNJ 1020

F i Pl (2D

Problem 2-12

The component of force F acting along line aa is require to be Fa. Determine the magnitude of F

and its component along line bb.

Given:

Fa 30N

θ1=80deg

θ2=60deg

ANS :

F = 19.2N

FB = 26.4N

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Statics BNJ 1020

F i Pl (2D

Problem 2-13

A resulatant force F is necessary to hold the ballon in place. Resolve this force into components

along the tether lines AB and AC , and compute the magnitude of each component.

Given:

F 350N

θ1 30deg

θ2 40deg

ANS :

FAB = 186N

FAC = 239N

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Statics BNJ 1020

F i Pl (2D

Problem 2-14

The post is to be pulled out of the ground using two ropes A and B. Rope A is subjected to force F1

and is directed at angle θ 1 from the horizontal. If the resultant force acting on the post is to be

FR , vertically upward, determine the force T in rope B and the corresponding angle θ

Given:

FR 1200N

F1 600N

θ1 60deg

ANS :

T = 744N

θ 23.8 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-15



Given:

F1 250N

F2 150N

θ1 30deg

θ2 30deg

θ3 105deg

ANS :

F1V = 129N

F1U = 183N

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Statics BNJ 1020

F i Pl (2D

Problem 2-16



Given:

F1 250N

F2 150N

θ1 30deg

θ2 30deg

θ3 105deg

ANS :

F1V = 77.6N

F2U = 150N

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Statics BNJ 1020

F i Pl (2D

Problem 2-17

Determine the magnitude and direction of the resultant force FR ..Express the result in terms of

the magnitudes of the components F1 and F2 and the angle ϕ.

ANS :

FR = F12

F22

2F1⋅F2⋅cos( ϕ )

F1⋅sin( ϕ) tanθ = F2 F1⋅cos( ϕ)

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Statics BNJ 1020

F i Pl (2D

Problem 2-18

If the tension in the cable is F1, determine the magnitude and direction of the resultant force

acting on the pulley. This angle defines the same angle θ of line AB on the tailboard block.

Given:

F1 400N

θ1 30deg

ANS:

FR 400 N

θ 60.00 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-19

The riveted bracket supports two forces. Determine the angle θ so that the resultant force is

directed along the negative x axis. What is the magnitude of this resultant force?

Given:

F1 60N

F2 70N

θ1 30deg

ANS:

FR 115.2 N

θ 25.4 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-20

The plate is subjected to the forces acting on members A and B as shown. Determine the

magnitude of the resultant of these forces and its direction measured clockwise from the positive

x axis.

Given:

FA 400N

FB 500N

θ1 30deg

θ 60deg

ANS : FR 458 N

α 10.9 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-21

Determine the angle θ for connecting member B to the plate so that the resultant of FA and FB is

directed along the positive x axis. What is the magnitude of the resultant force?

Given:

FA 400N

FB 500N

θ1 30deg

ANS : FR 561 N

θ 43.9 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-23

Determine the magnitude and direction of the resultant FR = F1 + F2 + F3 of the three forces by

first finding the resultant F' = F2+F3 and then forming FR = F' + F1.

Given:

F1 30N

F2 20N

F3 50N

θ 20deg

c 3

d 4

ANS : F' 47.07 N β = 47.07 deg , FR 19.2 N, ψ 2.37 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-24

Resolve the force F into components acting along (a) the x and y axes, and (b) the x and y' axes.

Given:

F 500N

α 65deg

β 45deg

γ 30deg

ANS:

(a) Fx 353.6 N

FY = 353.6 N

(b) Fx 149.4 N, Fy' 408.2 N

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Statics BNJ 1020

F i Pl (2D

Problem 2-25

The boat is to be pulled onto the shore using two ropes. Determine the magnitudes of forces T

and P acting in each rope in order to develop a resultant force F1, directed along the keel axis aa as shown.

Given:

θ 40deg

θ1 30deg

F1 400N

ANS : T 273.6 N, P 212.8 N

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Statics BNJ 1020

F i Pl (2D

Problem 2-26

The boat is to be pulled onto the shore using two ropes. If the resultant force is to be F1, directed

along the keel aa as shown, determine the magnitudes of forces T and P acting in each rope and

the angle θ of P so that the magnitude of P is a minimum. T acts at θ from the keel as shown.

Given:

θ1 30deg

F1 400N

ANS :

P 200 N T 346.4 N

θ 60 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-27

The beam is to be hoisted using two chains. Determine the magnitudes of forces FA and FB

acting on each chain in order to develop a resultant force T directed along the positive y axis.

Given:

T 600N

θ1 30deg θ 45deg

ANS : FA 439 N

FB 311 N

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Statics BNJ 1020

F i Pl (2D

Problem 2-28

The beam is to be hoisted using two chains. If the resultant force is to be F, directed along the

positive y axis, determine the magnitudes of forces FA and FB acting on each chain and the

orientation θ of FB so that the magnitude of FB is a minimum.

Given:

F 600N

θ1 30deg

ANS : FA 520 N

FB 300 N

θ 60 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-29

Three chains act on the bracket such that they create a resultant force having magnitude FR . If

two of the chains are subjected to known forces, as shown, determine the orientation θ of the

third chain,measured clockwise from the positive x axis, so that the magnitude of force F in this

chain is a minimum. All forces lie in the x-y plane.What is the magnitude of F? Hint : First findthe resultant of the two known forces. Force F acts in this direction.

Given:

FR 500N

F1 200N

F2 300N

φ 30deg

ANS : FR1 264.6 N

F 235 N, θ 10.9 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-30

Three cables pull on the pipe such that they create a resultant force having magnitude FR . If two

of the cables are subjected to known forces, as shown in the figure, determine the direction θ of

the third cable so that the magnitude of force F in this cable is a minimum. All forces lie in the

x – y plane.What is the magnitude of F? Hint : First find the resultant of the two known forces.

Given:

FR 900N

F1 600N

F2 400N

α 45deg

β 30deg

ANS: F 97.4 N, θ 16.2 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-31

Determine the x and y components of the force F.

Given:

F 800N

α 60deg

β 40deg

ANS :

Fx 514 N

Fy −613 N

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Statics BNJ 1020

F i Pl (2D

Problem 2-32

Determine the magnitude of the resultant force and its direction, measured clockwise from the

positive x axis.

Given:

F1 70N

F2 50N

F3 65N

θ 30deg

φ 45deg

ANS :

FR 97.8 N

θ 46.5 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-33

Determine the magnitude of the resultant force and its direction measured counterclockwise

from the positive x axis.

Given: F1

50N

F2

35N

α 120deg

β 25deg

ANS : FR 29.3 N, θ 347 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-34

Determine the magnitude of the resultant force and its direction , measured counterclockwise


Given:

F1 850N

F2 625N

F3 750N

θ 45deg

φ 30deg

c 3

d 4

ANS :

FR 546 N,β 253 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-35

Three forces act on the bracket. Determine the magnitude and direction θ of F1 so that the

resultant force is directed along the positive x' axis and has a magnitude of FR .

Units Used:

kN 103

N

Given:

FR 1kN

F2 450N

F3 200N

α 45deg

β 30deg

ANS : F1 889 N,

θ 37 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-36

Determine the magnitude and direction , measured counterclockwise from the x' axis, of the

resultant force of the three forces acting on the bracket.

Given:

F1 300N

F2 450N

F3 200N α 45deg β 30deg θ 20deg

ANS : FR 717 N

φ' 37.1 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-37

Determine the magnitude of the resultant force and its direction, measured counterclockwise


Given:

F1 800N

F2 600N

θ 40deg

c 12

d 5

ANS :

FR 747 N

θ 85.5 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-38

Determine the magnitude of the resultant force and its direction, measured counterclockwise


Units Used:

kN 103

N

Given:

F1 30kN F2 26kN

θ 30deg c 5

d 12

ANS : FR 25.1 kN

φ 4.53 deg

β 184.53 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-39

Determine the magnitude of the resultant force and its direction measured counterclockwise


Given:

F1 60N

F2 70N

F3 50N

θ1 60deg θ2 45deg c 1

d 1

ANS :

FR 111.5 N

θ 157.55 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-40


counterclockwise from the positive x axis by summing the rectangular or x, y components of the

forces to obtain the resultant force.

Given:

F1 600N

F2 800N

F3 450N

θ1 60deg

θ2 45deg

θ3 75deg

ANS:

FR 867 N

θ 108 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-41

Determine the magnitude and direction of the resultant FR = F1 + F2 + F3 of the three forces by

summing the rectangular or x, y components of the forces to obtain the resultant force.

Given:

F1 30N

F2 20N

F3 50N

θ 20deg

c 3

d 4

ANS : FR 19.2 N, θ 2.37 deg

Problem 2-42

Determine the magnitude and orientation, measured counterclockwise from the

positive y axis, of the resultant force acting on the bracket.

Given:

FA 700N

FB 600N

θ 20deg

φ 30deg

ANS : FR 839 N, θ 14.8 deg

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Statics BNJ 1020

F i Pl (2D

Problem 2-43

Determine the magnitude and direction, measured counterclockwise from the positive x' axis, of

the resultant force of the three forces acting on the bracket.

Given:

F1 300N

F2 200N

F3 180N

θ 10deg

θ1 60deg c 5

d 12

ANS : FR 389 N

ψ 42.7 deg

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Problem 2-44

Determine the x and y components of F1 and F2.

Given:

F1 200N

F2 150N

θ 45deg

φ 30deg

ANS : F1x 141 N

F1y 141 N

F2x −130 N

F2y 75 N

Problem 2-45

Determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive

x axis.

Given:

F1 200N

F2 150N

θ 45deg

φ 30deg

ANS : FRx 11.518 N

FRy 216.4 N

F 217 N

β 87 deg

Tutorial 2 Feb 2016

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